宇宙的初始条件：正弦模式的符号
Initial conditions of the universe: A sign of the sine mode
摘要：
在标准的大爆炸模型中，宇宙开始于辐射主导的时代，其中引力摄动由二阶微分方程描述，通常有两组正交的解。一种是所谓的{ \it增长（余弦）}模式，另一种是{ \it衰减（正弦）}模式，其中命名是从它们在超视界（亚视界）尺度上的行为中得出的。随着时间的推移，衰减模式在\emph{super-horizon}尺度上的演化与绝热扰动的增长模式有本质的不同。在同步规范和牛顿规范中分析了这种模式对超视界尺度的时间依赖性，以了解这些模式的真实规范不变行为。然后，我们探索这种模式的幅度之间的尺度上的限制$k \sim 10^{-5}$ Mpc $^{-1}$和$k \sim 10^{-1}$ Mpc $^{-1}$使用的温度和偏振各向异性从宇宙微波背景，通过计算Fisher信息。将原始功率非参数化地分成100个仓，我们发现衰减模式被约束在可比的方差上，作为使用温度各向异性的尺度小于今天的地平线上的增长模式。增加偏振数据使得衰减模式更受约束。因此，衰减模式振幅受到增长模式的$\sim 1/l$的约束。在超地平线尺度上，增长模式受到很差的约束，而衰减模式不能大大超过尺度不变的幅度。这种解释与过去文献中引用规范依赖变量的约束有很大不同，导致了虚幻的紧超视界衰减模约束。这里给出的结果通常可以用来非参数约束任何早期宇宙模型。
英文摘要：
In the standard big bang model the universe starts in a radiation dominated era, where the gravitational perturbations are described by second order differential equations, which will generally have two orthogonal set of solutions. One is the so called {\it growing(cosine)} mode and the other is the {\it decaying(sine)} mode, where the nomenclature is derived from their behaviour on super-horizon(sub-horizon) scales. The decaying mode is qualitatively different to the growing mode of adiabatic perturbations as it evolves with time on \emph{super-horizon} scales. The time dependence of this mode on super-horizon scales is analysed in both the synchronous gauge and the Newtonian gauge to understand the true gauge invariant behaviour of these modes. We then explore constraints on the amplitude of this mode on scales between $k \sim 10^{-5}$ Mpc$^{-1}$ and $k \sim 10^{-1}$ Mpc$^{-1}$ using the temperature and polarization anisotropies from the cosmic microwave background, by computing the Fisher information. Binning the primordial power non-parametrically into 100 bins, we find that the decaying modes are constrained at comparable variance as the growing modes on scales smaller than the horizon today using temperature anisotropies. Adding polrisation data makes the decaying mode more constrained. The decaying mode amplitude is thus constrained by $\sim 1/l$ of the growing mode. On super-horizon scales, the growing mode is poorly constrained, while the decaying mode cannot substantially exceed the scale-invariant amplitude. This interpretation differs substantially from the past literature, where the constraints were quoted in gauge-dependent variables, and resulted in illusionary tight super-horizon decaying mode constraints. The results presented here can generally be used to non-parametrically constrain any model of the early universe.
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